Question $1$ to Question $10$ is based on this question.

The GED Corporation manufactures two electrical devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires $2$ hours of wiring and $1$ hour of testing and can be sold for a $$250$ profit. Each alternator requires $3$ hours of wiring and $2$ hours of testing and can be sold for a $$150$ profit. There are $260$ hours of wiring and $140$ hours of testing time available in the next production period and GED wants to maximize profit.

The LP formulation is as follows:

Let X$1=$ Number of generators to produce

X$2=$ Number of alternators to produce

Max $250$X$1+150$X$2$

Subject to:

$2$X$1+3$X$2<=260($Wiring$)$

$1$X$1+2$X$2<=140($Testing$)$

X$1,$ X$2>=0$

Implement the above LP problem in Excel. Use Solver to solve the problem and create a Sensitivity Report. Use this information to answer the following questions:

Question $1$: What is the optimal solution?

A$.$X$1=100,$ X$2=20$

B$.$X$1=0,$ X$2=70$

C$.$X$1=130,$ X$2=0$

D$.$X$1=120,$ X$2=30$

E$.$ X$1=0,$ X$2=0$

Question $2$: What is the optimal objective function value?

A$.28000$

B$.10500$

C$.32500$

D$.34500$

E$.0$

Question $3$: Which value can the unit profit of generator be without changing the optimal solution?

A$.90$

B$.500$

C$.20$

D$.5$

Question $4$: Which value can the unit profit of alternator be without changing the optimal solution?

A$.350$

B$.400$

C$.550$

D$.800$

Question $5$: Which of the following statement is not true?

A$.$ The allowable decrease in X$1$ is $150$ which means if the objective function coefficient for X$1$ is less than $100$ the optimal solution will change.

B$.$ The allowable increase in X$2$ is $225$ which means if the objective function coefficient for X$2$ is larger than $375$ the optimal solution will change.

C$.$The optimal solution to this problem is unique.

D$.$ There are multiple optimal solutions to this problem.

Question $6$: If we force X$2$ to be $1,$ the optimal objective function value will $\_\_\_\_\_\_\_\_\_$ Hint: Think about the definition of reduced cost

A$.$ decrease by $225$

B$.$ increase by $225$

C$.$ decrease by by $150$

D$.$ decrease by $125$

Question $7$: Which statement regarding the shadow price of the Testing time constraint is true?

A$.$The shadow price of the second constraint is positive because the shadow price of a slack constraint is always positive.

B$.$The shadow price of the second constraint is negative because the shadow price of a slack constraint is always negative.

C$.$The shadow price of the second constraint is zero because the shadow price of a slack constraint is always $0.$

D$.$There is no way to know about the shadow price of the second constraint without the sensitivity report.

Question $8$: What is the optimal objective function value if the wiring time availability changes from $260$ to $270?$

A$.33750$

B$.19950$

C$.36000$

D$.10350$

Question $9$: What is the reduced cost of alternator if it only needs $2$ hours of wiring?

A$.100$

B$.25$

C$.0$

D$.-25$

E$.-100$

If alternator only needs $2$ hours of wiring instead of $3$ hours, which statement is true?

A$.$ It will be worthwhile to produce alternator because the reduced cost will be positive.

B$.$It will be not worthwhile to produce alternator because the reduced cost will be positive.

C$.$ It will be worthwhile to produce alternator because the reduced cost will be negative.

D$.$ It will be not worthwhile to produce alternator because the reduced cost will be negative.

E$.$ It will be not worthwhile to produce alternator because the reduced cost will be zero.